The conventional ultrasound medium characteristic measuring apparatus utilizes dependency on frequency of attenuation and reflection. For example, when measuring living body tissue the received reflected wave, in the frequency domain is often analyzed.
A reflection signal corresponding to a minute region (3.about.10 mm) between the depths z.sub.1 and z.sub.1 +.DELTA.z (FIG. 1) is extracted with a time gate from a series of reflection signals. The reflected signals are obtained by sending the ultrasound pulse, with a center frequency of 2.about.10 MHz and pulse length (duration) of about 1 .mu.s, into a medium from the surface of the medium. Pulses reflected from respective depths of the medium are received and such reflected signals are analyzed as an echo signal, indicating tissue characteristics of the depth z.sub.1. The depth z and time unit t of the reflected signal are related to the velocity of sound C of medium and expressed by the following equation: EQU t=2z/C
An echo signal is converted to a power spectrum S(f) in the frequency domain by Fourier transform means, such as an FFT (Fast Fourier Transformer). Generally, many reflectors exist within the small domain and the reflected pulses from respective reflectors are superposed on each other and interfere with each other. Thus, the echo signal has a complicated waveform and its power spectrum takes a form where a spectrum .vertline.R(f).vertline..sup.2, which can be seen as noise having random unevenness, is multiplied to the spectrum S.sub.0 (f) of a reflected wave having a unit intensity reflected from one reflector. This concept is discussed dependent reflection factors in ultrasonic bio-tissue characterization" Proc. 1984 International Symp. on noise and clutter rejection in radars and imaging sensors. pp. 158-163, October 1984. This random spectrum .vertline.R(f).vertline..sup.2 is called a scallop power spectrum and is expressed as the following equation (1): EQU .vertline.R(f).vertline..sup.2 =R.sub.0.sup.2 (1+.delta..sub.(f)) (1)
R.sub.0.sup.2 is a power reflection intensity of the entire part of the small domain and .delta..sub.(f) is a relative fluctuation of random frequency characteristic. The average value .delta..sub.(f) of the relative fluctuation of random frequency characteristics is 0. In this case, power spectrum of echo S.sub.(f) is given by the following equation (2): EQU S.sub.(f) =S.sub.0(f) .vertline.R.sub.(f) .vertline..sup.2 =S.sub.0(f) .vertline.R.sub.0(f) .vertline..sup.2 (1+.delta..sub.(f))=S.sub.(f) (1+.delta..sub.(f)) (2)
Where, EQU S.sub.(f) =S.sub.0 (f).multidot.R.sub.0.sup.2.sub.(f)
S.sub.(f) includes attenuation in both a travelling and returning direction to and from the depth z where the domain exists. An average reflection characteristic of such domain and .delta..sub.(f) has information about the arrangement of random reflectors within the domain. For the measurement of characteristic values such as attenuation coefficient and average reflection coefficient, etc., the scallop factor .delta..sub.(f) becomes an error factor.
In order to eliminate adverse influence of .delta..sub.(f), a statistical average has been utilized. For this purpose, the power spectrums of k domains in the periphery, which are assumed to have the same property as the object domain, are obtained and the simple additional average is obtained from them. Thereby, diversion V.sub.[.delta.] of average value of 1+.delta..sub.(f) is reduced to 1/k by average means of k power spectrums. However, this method requires about 100 domains as a value of k in order to obtain sufficient accuracy from the point of view of diagnosis when, for example, measuring a proportional constant for the frequency in the attenuation coefficient .alpha. (in a living body, it is known that .alpha.=.beta.F, .beta. being the attenuation slope). The time window width (corresponding to .DELTA.z) must be substantially wider than the pulse length in order to correctly obtain the spectrum. That is, the time window width should be about 10 .mu.s for a pulse length of about 1 .mu.s and it can be converted to the length of domain of about 7.5 mm when the sound velocity is assumed as 1500 m/s. The diameter of an ultrasound beam is 3.about.5 mm in the frequency range used in diagnosis. Therefore, for example, when the k domains (m.times.n, where m domains on a single scanning line as the particular interest domains and n scanning lines) are selected for the ultrasound echo tomographic image, the domains are arranged into almost a square as a whole, where a square of about 5 cm.times.5 cm can be obtained when k.apprxeq.100, m.apprxeq.6.about.7, n.apprxeq.15. It has been a disadvantage in this method that selection of a wider domain within a single tissue is possible only in a large organ such as a liver. Moreover such selection cannot be adapted to a minute focal lesion such as tumor or initial stages of cancer, even in the liver, and it has been adapted only to diffusion lesion such as cirrhosis and fattiness.
Various attempts have been made to reduce the space required for measurement, namely by enhancing spatial resolution by suppressing as much as possible the random variable .delta..sub.(f) and reducing as much as possible the number of samples k required for a statistical average by a method other than the spacial statistic average. These attempts will then be explained hereunder.
The first method obtains a spectrum where spectrum scalloping is reduced by utilizing a homomorphic filter. By this method, a beta is obtained through various processings of the spectrum. Such a method is taught in U.S. Pat. No. 4,545,250 to Miwa, the same inventor as that of the subject application. In this method, a logarithmic value ln S.sub.(f) (common logarithm or dB may be used) of power spectrum S.sub.(f) is obtained, is then Fourier-transformed into cepstrum, and the desired processings such, as application of a low-pass window, obtaining a moving average, and smoothing by median filter (described later) are carried out. The processed cepstrum is then reverse Fourier-transformed into the logarithmic power spectrum ln S.sub.p(f), moreover, the power spectrum S.sub.p(f) is obtained after the processing and after obtaining the reverse logarithm, and the attenuation coefficient is obtained from such S.sub.p(f). In S.sub.p(f), .delta..sub.(f) is suppressed in comparison with S.sub.(f). Miwa '250 discloses the processing of the smoothing of the power spectrum on the cepstrum, not the processing on the logarithmic power spectrum. The smoothing of the power spectrum is processed directly in the present invention. Most of the processings disclosed in the prior art are linear processings, although some nonlinear processings are also included. Moreover, among the processing methods disclosed in the prior art, only the low-pass window processing is effective for the smoothing process on the cepstrum.
The second method fits a model spectrum to the raw spectrum S.sub.(f), obtained by the actual measurement of the spectrum, or logarithmic spectrum ln S.sub.(f) by formulating such model spectrum. For example, in such a model that the attenuation coefficient .alpha.=.beta.f, .beta. is constant between the depth z.sub.1 and depth z.sub.2, namely between D=z.sub.2 -z.sub.1 and dependency on frequency of reflection coefficient at the depths z.sub.1, z.sub.2 is equal. Accordingly, the (3) following relations can be obtained: ##EQU1##
Where, .delta..sub.1(f) is a random variable of equation (1) at the depth z.sub.1 and .delta..sub.2(f) is a similar random variable at the depth z.sub.2. The left side of equation (3) is actually a measured value. The first item in the right side is the spectrum of frequency modeled to the linear function, and the second and third items on the right side of the equation are random variables which become the random variables .epsilon..sub.(f) in equation (3-1). The above method is discussed in R. Kuc et al "Estimating the Acoustic Attenuation Coefficient slope for liver from reflected ultrasound signals" IEEE, SU-26, No. 5, pp. 353-362, September 1979. As is well known, any linear function of a variable f can be expressed as pf+q, where p and q are coefficients defined for each linear function. In this case, the linear equation pf+q is curve-fitted to the plot as the frequency function of the actually measured value in the left side of equation (3) by the least mean square error method and a value .beta. is obtained from the slope p. This is called the spectrum difference method and is discussed in an article by R. Kuc entitled "Estimating acoustic attenuation from reflected ultrasound signals; comparison of spectral shift and spectral-differences approach, IEEE ASSP-32 No. 1, pp. 1-6, February 1984.
A Gaussian distribution is assumed for the send spectrum in addition to the modeling of linear attenuation coefficient .alpha.=.beta.f for frequency, and dependency on frequency of reflection coefficients of z.sub.1,z.sub.2 is also assumed equal. Both S.sub.1(f) and S.sub.2(f) show the Gaussian distributions of the center frequencies of such spectrums becoming f.sub.01, f.sub.02, and the divergence of spectrum, namely the standard deviation .sigma. is equal in such spectrums. Moreover, there is a relation expressed by the following equation (4) between these two center frequencies. In addition, .beta. can be obtained from the equation (4) and this is called the center frequency transition method. EQU f.sub.01 -f.sub.02 =4.sigma..sup.2 .beta.D (4)
f.sub.01, f.sub.02 can be determined respectively from the 0th moment and primary moment of the spectrums of S.sub.1(f). The S.sub.2(f) and the method of obtaining .beta. from f.sub.01, f.sub.02 thus obtained is called the moment method.
The logarithm of the equation (2) can be obtained from the following equation (5) and the item (1+.delta..sub.(f)) is not the multiplication item but becomes the addition item as indicated below. EQU ln S.sub.(f) =ln S.sub.(f) +ln (1+.delta..sub.(f))=ln S.sub.(f) +n(f) EQU n(f)=ln (1+.delta..sub.(f) ( 5)
ln (f), namely ln (1+.delta..sub.(f)) is a random variable, an average value becomes a constant value h.sub.n and n(f) becomes a random variable fluctuating around the average value. When S.sub.(f) is the Gaussian distribution, ln S.sub.(f) becomes a parabolic equation of f and the parabolic equation pf.sup.2 +qf+r can be curve-fitted to the actually measured value in the left side by the least mean square error method because n.sub.(f) becomes uniform additional random variables for the frequency. The center frequency f.sub.0 of the Gaussian distribution and frequency standard deviation .sigma. can be obtained from these p and q. EQU 2.sigma..sup.2 =-1/p, f.sub.0 =-q/2p (6)
A value of .beta. can be obtained by substituting f.sub.0 of the equation (6) into the equation (4). This method is called the parabola application method R. Kuc "bounds on estimating the acoustic attenuation of small tissue regions from reflected ultrasound" IEE Proceedings to be published.
In the model of Gaussian spectrum and attenuation coefficient of frequency linearity, the frequency standard deviation .sigma. becomes a constant value as explained above. R. Kuc has announced the method that the parabolas (-1/2.sigma..sup.2)f.sup.2 +(2f.sub.0 /2.sigma..sup.2)f+r, (.sigma..sup.2 : constant) having the constant coefficient of f.sup.2, form various f.sub.0. These are correlated with the left side of the equation (5) and a value of .beta. is obtained considering f.sub.0 which makes maximum the correlated value as the center frequency. This method is called the correlation method or Matched-filter method.
Here, various methods described above are compared. In any of the spectrum difference method in the logarithm spectrum region, the parabola application method and the matched filter method, the model spectrum, not including random variables, is fitted to the spectrum, including random variables by linear processing.
The inventors of the present invention have investigated, by computer simulation, the influence on the value .beta. of the scallop by applying the spectrum difference method and parabola application method to the pseudo echo signal generated from the line of random reflectors. This confirmed that there is no particular difference between these methods.
R. Kuc has also investigated an error of value of .beta. caused by scalloping in the same way as above for the simple moment method where a value .beta. is extracted directly from the moment of the power spectrum of true value region, the matched filter (correlation) method, the Zero-Cross-Density method which is one of the time region processing and also made it obvious that the accuracy of the spectrum difference method and the matched filter method is more better than that of the other two methods and said two methods provide almost the same accuracy.
The inventors of the patent invention have attempted the technique by the inventors of smoothing the logarithmic spectrum by use of a moving average of adjacent spectral points and then adopting the spectral difference method or the parabolic method or its correlation-maximization variant to produce the local beta value. Regarding spatial/temporal resolution, the obtained results have little improvement over beta obtained from these methods using directly measured values and the aforementioned statistical averaging.
From the above explanation, it is obvious that the spectrum difference method, parabola application method and matched filter method on the logarithm spectrum are the best methods and these three methods give the same accuracy of the value of .beta.. R. Kuc has indicated that the spatial average is still necessary when measuring with such best methods and the ultrasound apparatus for diagnosis which can be used practically has the limit of theoretical space resolution of 2 cm.times.2 cm.
However, as the diagnostic apparatus, such resolution of 2 cm.times.2 cm is still insufficient. For example, resolution of at least 1 cm.times.1 cm or less is necessary for judging that a tumor is malignant or benign. When a cancer of 1 cm or larger is found, it often has already spread to another part of the body. As explained above, the conventional method has a disadvantage that it gives insufficient space resolution. Moreover, a statistical average method takes a longer time for measurement and is inferior in practical use.
The present invention is intended to reduce and improve such disadvantages of the prior arts.